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C:\test>rand -M=7 -N=1e5
{ "0" => 13948, 1 => 14522, 2 => 14752, 3 => 14208, 4 => 14032, 5 => 1
+4408, 6 => 14130 }
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C:\test>rand -M=100 -N=1e5
{ "0" => 1029, 1 => 1110, 2 => 977, 3 => 1031, 4 => 1008, 5 => 1137, 6
+ => 998, 7 => 1169, 8 => 915, 9 => 1039, 10 => 879, 11 => 1149, 12 =>
+ 967, 13 => 972, 14 => 954, 15 => 967, 16 => 1219, 17 => 1009, 18 => 
+870, 19 => 858, 20 => 1005, 21 => 1077, 22 => 914, 23 => 930, 24 => 9
+87, 25 => 951, 26 => 979, 27 => 1029, 28 => 1056, 29 => 902, 30 => 96
+5, 31 => 810, 32 => 979, 33 => 1101, 34 => 1009, 35 => 1190, 36 => 86
+8, 37 => 1013, 38 => 981, 39 => 1104, 40 => 905, 41 => 993, 42 => 937
+, 43 => 1018, 44 => 1098, 45 => 1053, 46 => 898, 47 => 908, 48 => 994
+, 49 => 1135, 50 => 1174, 51 => 1010, 52 => 967, 53 => 1025, 54 => 99
+5, 55 => 1029, 56 => 875, 57 => 1129, 58 => 908, 59 => 976, 60 => 906
+, 61 => 922, 62 => 962, 63 => 931, 64 => 1044, 65 => 999, 66 => 980, 
+67 => 838, 68 => 973, 69 => 1140, 70 => 949, 71 => 965, 72 => 1044, 7
+3 => 940, 74 => 927, 75 => 1107, 76 => 925, 77 => 1045, 78 => 968, 79
+ => 996, 80 => 890, 81 => 1123, 82 => 119
8 => 990, 89 => 966, 90 => 1072, 91 => 927, 92 => 915, 93 => 1093, 94 
+=> 1063, 95 => 966, 96 => 1056, 97 => 994, 98 => 844, 99 => 1086 }

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my $bytes = join '', map chr( unpack( 'V', $rand ) % 256 ), 1 .. $N;
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C:\test>rand -N=1e6
In 1e6 bytes, there are 3997975 ones and 4002025 zeros

C:\test>rand -N=1e6
...
...
In 1e6 bytes, there are 3991425 ones and 4008575 zeros
Stddev: 197.76
{ 2 => 500058, 3 => 248757, 4 => 124893, 5 => 62380, 6 => 30268, 7 => 
+24800, 8 => 4693, 9 => 582, 10 => 153, 11 => 59, 12 => 26, 13 => 13, 
+14 => 10, 15 => 11, 16 => 108, 17 => 45, 18 => 14, 19 => 11, 20 => 5,
+ 21 => 8, 22 => 7, 23 => 2, 24 => 46, 25 => 13, 26 => 10, 27 => 6, 28
+ => 5, 29 => 3, 30 => 3, 31 => 1, 32 => 50, 33 => 10, 34 => 6, 35 => 
+3, 36 => 5, 37 => 3, 38 => 1, 39 => 1, 40 => 40 }